Topic
Scalar curvature
About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.
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TL;DR: In this article, the authors studied the metric solutions for the gravitational equations in Modified Gravity Models (MGMs) and showed that the Newtonian limit is well defined as a limit at intermediate energies.
Abstract: We study the metric solutions for the gravitational equations in Modified Gravity Models (MGMs). In models with negative powers of the scalar curvature, we show that the Newtonian Limit (NL) is well defined as a limit at intermediate energies, in contrast with the usual low energy interpretation. Indeed, we show that the gravitational interaction is modified at low densities or low curvatures.
158 citations
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Abstract: This paper develops various estimates for solutions of a nonlinear, fourth order PDE which corresponds to prescribing the scalar curvature of a toric K?ahler metric The results combine techniques from Riemannian geometry and from the theory of MongeAmp` ere equations
158 citations
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TL;DR: In this article, a dual one-to-one correspondence between the candidates of the two concepts is shown. And they show that Fisher information is obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.
Abstract: Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show that there is a kind of dual one-to-one correspondence between the candidates of the two concepts. We emphasize that Fisher information is obtained from relative entropies as contrast functions on the state space and argue that the scalar curvature might be interpreted as an uncertainty density on a statistical manifold.
157 citations
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TL;DR: In this paper, the first two terms of the power series expansion for Fro(r) are computed for surfaces in RS and the coefficients of r n+~ for/r even can be expressed in terms of curvature.
Abstract: (Here o~-~the volume of the unit ball in R\". The simplest expression for eo is w = (1]( 89 \"/~ where ({rn)! ---F( 89 + 1).) First we make several remarks. 1. Our method for attacking the conjecture (I) will be to use the power series expansion for Vm(r). This expansion will be considered in detail in section 3; however, the general facts about it are the following: (a) the first term in the series is corn; (b) the coefficient of r n+~ vanishes provided k is odd; (c) the coefficients of r n+~ for/r even can be expressed in terms of curvature. Unfortunately the nonzero coefficients depend on curvature in a rather complicated way, and this is what makes the resolution of the conjecture (I) an interesting problem. 2. To our knowledge the power series expansion for Vm(r) was first considered in 1848 by Bertrand-Diguet-Puiseux [6]. See also [14, p. 209]. In these papers the first two terms of the expansion for Fro(r) are computed for surfaces in RS:
157 citations
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TL;DR: In this paper, a Lagrangian derivation of the Equations of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented.
Abstract: A Lagrangian derivation of the Equations of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits one to reduce the EOM to a single equation and we show how it is possible to construct exact solutions in F(R)-gravity. All known exact solutions are recovered. We also exhibit a new non-trivial solution with non-constant Ricci scalar.
157 citations